Basis property of a Rayleigh beam with boundary stabilization

A Rayleigh beam equation with boundary stabilization control is considered. Using an abstract result on the Riesz basis generation of discrete operators in Hilbert spaces, we show that the closed-loop system is a Riesz spectral system; that is, there is a sequence of generalized eigenfunctions of the system, which forms a Riesz basis in the state Hilbert space. The spectrum-determined growth condition, distribution of eigenvalues, as well as stability of the system are developed, This paper generalizes the results in Ref. 1.